Rate-Optimal Streaming Codes Under an Extended Delay Profile for Three-Node Relay Networks With Burst Erasures

TL;DR

This paper develops rate-optimal streaming codes for three-node relay networks with burst erasures, extending previous methods to broader delay profiles and identifying conditions where optimality is achievable.

Contribution

It introduces an extended delay profile method that achieves optimal rate under relaxed constraints, surpassing previous restrictions.

Findings

Achieves optimal rate under new delay profile constraints.

Identifies conditions where optimal rate is not achievable.

Extends previous coding strategies to broader scenarios.

Abstract

This paper investigates streaming codes for three-node relay networks under burst packet erasures with a delay constraint $T$. In any sliding window of $T+1$ consecutive packets, the source-to-relay and relay-to-destination channels may introduce burst erasures of lengths at most $b_1$ and $b_2$, respectively. Let $u = \max\{b_1, b_2\}$ and $v = \min\{b_1, b_2\}$. Singhvi et al. proposed a construction achieving the optimal rate when $u\mid (T-u-v)$. In this paper, we present an extended delay profile method that attains the optimal rate under a relaxed constraint $\frac{T - u - v}{2u - v} \leq \left\lfloor \frac{T - u - v}{u} \right\rfloor$ and it strictly cover restriction $u\mid (T-u-v)$. %Furthermore, we demonstrate that the optimal rate for streaming codes is not achievable when $0< T-u-v<v$ under the convolutional code framework.